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Article

Keywords:
heat equation; boundary value problem; heat potential; density
Summary:
The Fourier problem on planar domains with time moving boundary is considered using integral equations. Solvability of those integral equations in the space of bounded Baire functions as well as the convergence of the corresponding Neumann series are proved.
References:
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[2] M. Dont: On a boundary value problem for the heat equation. Czechoslovak Math. J. 25 (1975), 110-133. MR 0369919 | Zbl 0304.35052
[3] M. Dont: A note on a heat potential and the parabolic variation. Časopis Pěst. Mat. 101 (1976), 28-44. MR 0473536 | Zbl 0325.35043
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[7] W. L. Wendland: Boundary element methods and their asymptotic convergence. Lecture Notes of the CISM Summer-School on Theoгetical acoustic and numerical techniques, Int. Centre Mech. Sci., Udine (P. Filippi, ed.). Springer-Verlag, Wien, New York, 1983, pp. 137-216. MR 0762829 | Zbl 0618.65109
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